(a).

The function of the velocity is .

Prove that the accelertaion is proportional to velocity.

The function is .

The acceleration of the function is derivative of the velocity, hence .

Apply derivative with respect to .

.

Therefore, the accelertaion is proportional to velocity.

(b)

The function of the velocity is .

Where,  is the initial velocity or the velocity at time .

(c)

Find the time when the velocity equal to half the initial velocity.

Substitute .

 is the initial velocity or the velocity at time  , hence .

Substitute aabove value in .

Therefore,the velocity equal to half the initial velocity at time .

(a) The accelertaion is proportional to velocity.

(b)  is the initial velocity or the velocity at time .

(c) The velocity equal to half the initial velocity at time .